What is the median of the numbers 4, 7, 9, 12, 15, 18 ?
Answer: B
Correct answer: 10.5
The values are already in ascending order and there are six of them, an even count, so the median is the mean of the third and fourth.
\[\frac{9 + 12}{2} = 10.5\]
With an even number of observations the median need not be one of the values in the list.
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The average salary of 15 persons is Rs. 5500. If the salary of one person is added, the average increases to Rs. 5700. What is the salary of this one person?
Answer: A
Total salary of 15 persons = 15 × 5500 = 82500.
Total salary of 16 persons = 16 × 5700 = 91200.
Salary of the new person = 91200 - 82500 = 8700.
Alternatively, the new person must bring his own average (5700) plus enough to raise the average of the other 15 people by 200 each. Salary = 5700 + 15 * 200 = 5700 + 3000 = 8700.
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Find the median of the first 10 prime numbers.
Answer: B
The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Since there are 10 numbers (an even count), the median is the average of the two middle numbers (the 5th and 6th).
5th number = 11.
6th number = 13.
Median = \(\frac{11+13}{2} = \frac{24}{2} = 12\).
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In a negatively skewed distribution, the correct inequality is:
Answer: A
In a negatively (left) skewed distribution, the tail is on the left side. The extreme low values pull the mean to the left.
The order of the central tendencies is: Mean < Median < Mode.
Conversely, in a positively skewed distribution, the order is Mode < Median < Mean.
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The mean of 100 observations was calculated as 40. It was found later on that one of the observations was misread as 83 instead of 53. The correct mean is:
Answer: B
The incorrect sum of observations = 100 × 40 = 4000.
The difference due to misreading = Incorrect value - Correct value = 83 - 53 = 30.
The calculated sum is 30 more than the actual sum.
Correct sum = 4000 - 30 = 3970.
Correct mean = \(\frac{3970}{100} = 39.7\).
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The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
Answer: B
We are given the following equations from the averages:
1) P + Q = 2 × 5050 = 10100
2) Q + R = 2 × 6250 = 12500
3) P + R = 2 × 5200 = 10400
Adding all three equations: 2(P + Q + R) = 10100 + 12500 + 10400 = 33000.
So, P + Q + R = 16500.
To find P, we subtract equation (2) from this sum: P = (P+Q+R) - (Q+R) = 16500 - 12500 = 4000.
The monthly income of P is Rs. 4000.
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Find the geometric mean of 2, 4, and 8.
Answer: A
The geometric mean of \( n \) numbers is the \( n \)th root of their product.
\[ \sqrt[3]{2 \times 4 \times 8} = \sqrt[3]{64} = 4 \]
The arithmetic mean would be \( \tfrac{14}{3} = 4.67 \) - the first distractor.
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A data set can have:
Answer: D
A data set's mode has the following properties:
Therefore, all of the above statements are possible.
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The average of 7 consecutive numbers is 20. The largest of these numbers is:
Answer: D
For an odd number of consecutive terms, the mean (average) is the middle term.
Here, the average of 7 numbers is 20, so the 4th term is 20.
The numbers are: 17, 18, 19, 20, 21, 22, 23.
The largest number is 23.
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If the mean and median of a set of numbers are 12 and 15 respectively, then the mode is approximately:
Answer: B
\[ \text{Mode} = 3\,\text{Median} - 2\,\text{Mean} \]
\[ = 3(15) - 2(12) = 45 - 24 = 21 \]
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